SOLUTION: Three of Santa's helpers are a combined height of eleven feet and three inches. William is twelve inches shorter than Timothy, who is nine inches taller than James. How tall is eac

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Question 697589: Three of Santa's helpers are a combined height of eleven feet and three inches. William is twelve inches shorter than Timothy, who is nine inches taller than James. How tall is each of Santa's helpers?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let William's height = +w+
Let Timothy's height = +t+
Let James' height = +j+
given:
(1) +w+%2B+t+%2B+j+=+11.25+
( note that 3" is 1/4 of a foot )
(2) +w+=+t+-+1+
( 12" is 1 foot )
(3) +t+=+j+%2B+.75+
( 9" is 3/4 of 1 foot )
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This is 3 equations and 3 unknowns, so it's solvable
Substitute (2) into (1)
(1) +w+%2B+t+%2B+j+=+11.25+
(1) +t+-+1+%2B+t+%2B+j+=+11.25+
and
(3) +t+=+j+%2B+.75+
(2) +j+=+t+-+.75+
Substitute (2) into (1)
(1) +t+-+1+%2B+t+%2B+t+-+.75+=+11.25+ ( all units are in feet )
(1) +3t+-+1.75+=+11.25+
(1) +3t+=+13+
(1) +t+=+13%2F3+
and, since
(2) +j+=+t+-+.75+
(2) +j+=+13%2F3+-+3%2F4+
(2) +j+=+52%2F12+-+9%2F12+
(2) +j+=+43%2F12+
and
(1) +w+%2B+t+%2B+j+=+11.25+
(1) +w+%2B+13%2F3+%2B+43%2F12+=+11.25+
(1) +w+%2B+52%2F12+%2B+43%2F12+=+45%2F4+
(1) +w+%2B+95%2F12+=+135%2F12+
(1) +w+=+40%2F12+
(1) +w+=+10%2F3+
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William is 10/3 ft, or 3 ft 4 in
Timothy is 13/3 ft, or 4 ft 4 in
James is 43/12 ft, or 3 ft 7 in
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Hope I got it

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Three of Santa's helpers are a combined height of eleven feet and three inches. William is twelve inches shorter than Timothy, who is nine inches taller than James. How tall is each of Santa's helpers?

Let Timothy’s height be T
Then William’s is: T – 12, and James’ is: T – 9
Since 11’ 3” = 135”, then altogether:
T + T - 12 + T – 9 = 135
3T – 21 = 135
3T = 156
T, or Timothy is: 156/3, or 52”, or highlight_green%284_ft_4_inches%29 tall

William is 52 – 12, or 40”, or highlight_green%283_ft_4_inches%29 tall

James is: 52 – 9, or 43”, or highlight_green%283_ft_7_inches%29 tall

You can do the check!!

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